Non-orthogonal Data Region Boundaries for Big Data Discretization
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Solution Overview
Problem
Conventional data discretization methods often result in discretization errors due to orthogonal data region boundaries, which are not optimal for assigning data points to clusters, leading to inappropriate cluster assignments.
Innovation Solution
The implementation uses minimal surface theory to generate non-orthogonal data region boundaries, allowing for more accurate assignment of data points to discrete regions through the creation of a lookup table that maps data points to regions based on these boundaries.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If orthogonal data region boundaries are used for data discretization, then the data processing structure is simple and easy to implement, but discretization errors increase and data points may be assigned to inappropriate clusters
Solution Approach 1:
The patent applies curvature by transitioning from orthogonal (straight-line) boundaries to curved boundaries that follow the natural distribution of data points. The curved boundaries better accommodate the spherical or elliptical clusters in the data, reducing misclassification errors while maintaining computational feasibility through coordinate transformation methods.
Solution Approach 2:
The patent changes the parameter of boundary orientation from fixed orthogonal angles to variable angles that adapt to data distribution. By allowing boundary parameters to vary based on data characteristics, the system achieves higher discretization accuracy without sacrificing implementation feasibility, as the parameter changes are computed once during setup.
2Ease of manufacture
If conventional orthogonal boundaries are used, then the implementation is straightforward, but data velocity and processing efficiency are reduced
Solution Approach 1:
The patent applies preliminary action by pre-computing the curved boundaries and storing them in lookup tables before actual data processing. This upfront preparation allows the system to achieve high data velocity during operation by simply querying pre-computed boundaries rather than performing complex calculations for each data point, thus improving productivity without complicating the core processing logic.
Solution Approach 2:
The patent uses copying by creating lookup tables that store pre-computed boundary information. These tables serve as copies of the complex boundary definitions, allowing rapid data point assignment through simple table lookups rather than repeated complex geometric calculations, thereby significantly improving data processing velocity.
3Ease of operation
If data points are assigned based on closest centroid with orthogonal boundaries, then the assignment process is simple, but discretization errors occur and accuracy decreases
Solution Approach 1:
The patent replaces orthogonal boundaries with curved boundaries that better match the natural clustering of data points. This curvature allows data points near cluster edges to be assigned more accurately to their true clusters, improving measurement precision while maintaining operational simplicity through pre-computed lookup structures.
Solution Approach 2:
The patent substitutes the mechanical orthogonal boundary system with a mathematically optimized curved boundary system. By replacing the rigid orthogonal structure with flexible curved boundaries defined through coordinate transformations, the system achieves higher assignment accuracy while keeping the operational interface simple through lookup table queries.
Data Source
AI summary
Implementations generally relate to discretization for big data analytics. In some implementations, a method includes receiving a plurality of data points. The method further includes determining a plurality of data centroids, where each data centroid of the plurality of data centroids is predetermined. The method further includes determining a plurality of data regions for the plurality of data centroids, where each data region of the plurality of data regions is associated with a respective data centroid of the plurality of data centroids. The method further includes generating a plurality of data region boundaries for the plurality of data regions based at least in part on one or more data points of the plurality of data points, where each data region boundary of the plurality data region boundaries is associated with a respective data region of the plurality of data regions.